Getting out of sharepoint

I'm a teacher. We have a share point based learning environment. But our support system isn't working too well at the moment - communication wise.

I want to be able to create tests for my kids. I can do this easily nough either with an existing service or by writing a bespoke system in php and hosting it myself. The problem is logging in. I want o try and implement authorisation via sharepoint; the I'd logs in on sp, hits a link or iframe and is led seamlessly to my system where they are already logged in.